Question

Please help ASAP!!! Thank you so much!!! Just want confirm my answer it is y=150x-50. A concession stand at a football game took in $100 after being open for 1 hour. After 3 hours, the stand had taken in $400. Assuming a linear function, write an equation in the form y=mx+b that shows the revenue earned from being opened for x hours.

Answer 1

Answer: You have the correct answer. It is y = 150x-50

Nice work on getting the correct answer. For anyone curious, the explanation is below.

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x = number of hours the stand is open

y = amount earned

(1,100) is from the fact the stand is open 1 hour and earns $100

(3,400) is due to the stand earning $400 after 3 hours.

Slope Formula

m = (y2 - y1)/(x2 - x1)

m = (400-100)/(3-1)

m = 300/2

m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.

Use m = 150 and (x,y) = (1,100) to find the value of b as shown below

y = mx+b

100 = 150(1) + b

100 = 150 + b

100-150 = b

-50 = b

b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.

So we have m = 150 as the slope and b =  -50 as the y intercept.

Therefore, y = mx+b turns into y = 150x-50.

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As a check, plugging in x = 1 should lead to y = 100

y = 150x-50

y = 150(1)-50

y = 150-50

y = 100 and indeed it does

The same should be the case with (3,400). Plug in x = 3 and we should get y = 400

y = 150x-50

y = 150(3)-50

y = 450-50

y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).